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1、Chapter5AworldofrandomnessHowtheMarquisdeLaplacehadastrongintuitionthatwasprovedcorrectacenturyandahalflater,andhowmanyotherthingsthathappenedafterwardsweretoleaveaclearimprintinthedigitizedworld.Thestudyofmathematicalchanceisarelativelyrecentdevelopment.Dem-ocritus,aGreekphilosopher
2、,isoftencreditedasbeingtheearliestscholarofrandomphenomenaforhisassertionthattheuniversewasbornfromthecol-lisionsoftinyatomsagitatinginchaos.Lucretius,aRomanpoetandnaturalscientist,wentmuchfurther,givinganexplanationoftherestlessmotionoftheparticlesofdustinasunlightraythatanticipated
3、,withastonishingprecision,Einstein'stheoryofBrownianmotion.1Howevernoneoftheancientsagesseemtohavethoughtdeeplyaboutthemathematicalrulesofchance.Ran-domphenomenawereappreciatedinrelationtogambling,butitwasnotuntilthesixteenthcenturythatarealtreatiseonthetheoryofchanceappeared.Nowonde
4、rthattheauthor,aweirdoItalianwithmultiforminterests,wasahardenedgambler.HisnamewasGerolamoCardano,amathematicianandphysician,withabodydis guredbyoneoftherecurrentepidemicsofBlackDeaththattormentedEuropeinthosetimes,andaconsumingaddictiontogambling.InCardano'sbookLiberdeludoalee(TheBo
5、okofGamesofChance),aprimitiveversionofthetheoryofprobabilitywaslaiddown,alongthelinesfollowedbynearlyalltheothermathematiciansuntilthetwentiethcenturywhenthesestudiesweregivennew,strongerfoundations.WhatCardanoes-tablishedissomethingthatmaysoundveryfamiliar,thatis,theprobabilityofafa
6、vorableeventequalsthenumberofallfavorableeventsdividedbythenumberofallpossibleevents.Soforexampleifyoubetonanoutcomeof2onasixsideddie,yourchanceofwinningis1/6.Thisde nitionlastedforcenturies,butrequiresthatalleventsoccurwiththesameprobability(i.e.,1Lucretiuslivedinthe rstcenturyB.C.M
7、anyassertionscontainedinhispoemDeRerumNatura(OntheNatureofThings)haveprovedcorrectmanycenturieslater,althoughtheyarenotatallintuitive.Forexamplehestatedthatallbodieswouldfallwithequalaccelerationinthevacuum,althoughhecouldnotconductanyexperimenttovalidatehistheory.Allthisisdescribedi
8、nelegantvers
